TY - JOUR
T1 - ERROR ANALYSIS OF FORCED DISCRETE MECHANICAL SYSTEMS
AU - Fernandez, Javier
AU - Zurita, Sebastian Elias Graiff
AU - Grillo, Sergio
N1 - Funding Information:
This research was partially supported by grants from the Universidad Nacional de Cuyo (grants 06/C567 and 06/C574) and CONICET.
Publisher Copyright:
© 2021 American Institute of Mathematical Sciences. All rights reserved.
PY - 2021/12
Y1 - 2021/12
N2 - The purpose of this paper is to perform an error analysis of the variational integrators of mechanical systems subject to external forcing. Es- sentially, we prove that when a discretization of contact order r of the La- grangian and force are used, the integrator has the same contact order. Our analysis is performed first for discrete forced mechanical systems defined over TQ, where we study the existence of ows, the construction and properties of discrete exact systems and the contact order of the ows (variational integra- tors) in terms of the contact order of the original systems. Then we use those results to derive the corresponding analysis for the analogous forced systems defined over Q x Q.
AB - The purpose of this paper is to perform an error analysis of the variational integrators of mechanical systems subject to external forcing. Es- sentially, we prove that when a discretization of contact order r of the La- grangian and force are used, the integrator has the same contact order. Our analysis is performed first for discrete forced mechanical systems defined over TQ, where we study the existence of ows, the construction and properties of discrete exact systems and the contact order of the ows (variational integra- tors) in terms of the contact order of the original systems. Then we use those results to derive the corresponding analysis for the analogous forced systems defined over Q x Q.
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U2 - 10.3934/jgm.2021017
DO - 10.3934/jgm.2021017
M3 - Article
AN - SCOPUS:85122382803
VL - 13
SP - 533
EP - 606
JO - Journal of Geometric Mechanics
JF - Journal of Geometric Mechanics
SN - 1941-4889
IS - 4
ER -